1,124 research outputs found
Direction problems in affine spaces
This paper is a survey paper on old and recent results on direction problems
in finite dimensional affine spaces over a finite field.Comment: Academy Contact Forum "Galois geometries and applications", October
5, 2012, Brussels, Belgiu
A combinatorial characterisation of embedded polar spaces
Some classical polar spaces admit polar spaces of the same rank as embedded
polar spaces (often arisen as the intersection of the polar space with a
non-tangent hyperplane). In this article we look at sets of generators that
behave combinatorially as the set of generators of such an embedded polar
space, and we prove that they are the set of generators of an embedded polar
space
Gapless interface states at the junction between two topological insulators
We consider a junction between two topological insulators, and calculate the
properties of the interface states with an effective low energy Hamiltonian for
topological insulators with a single cone on the surface. This system bears a
close resemblance to bilayer graphene, as both result from the hybridization of
Dirac cones. We find gapless interface states not only when the helicity
direction of the topological surface states are oppositely oriented, but they
can also exist if they are equally oriented. Furthermore, we find that the
existence of the interface states can be understood from the closing of the
bulk gap when the helicity changes orientation. Recently, superluminal
tachyonic excitations were also claimed to exist at the interface between
topological insulators. However, here we show that these interface states do
not exist
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